Professor bunyan thinks he has discovered a remarkable property of binary search trees. suppose that the search for key kk in a binary search tree ends up in a leaf. consider three sets: aa, the keys to the left of the search path; bb, the keys on the search path; and cc, the keys to the right of the search path. professor bunyan claims that any three keys a \in aa∈a, b \in bb∈b, and c \in cc∈c must satisfy a \le b \le ca≤b≤c. give a smallest possible counterexample to the professor's claim.

Ihave a music player on my phone. i can buy songs, add them to playlists and play them. obviously it would be redundant to store each song in each playlist; each playlist is just a list of pointers to the songs. for this lab you will simulate this behavior. your program will need to have options to: add songs to the system library (you will store the text of the first line of the song, rather than the audio) add playlists add songs to a playlist list playlists play a playlist list all of the songs in the library with a count of how many times each song has been played remove a song from a playlist remove a playlist remove a song from the library (and thus from all playlists that contain it) note that we will not be checking many error cases. in real programming this would be bad, you should usually try to recognize and respond to as many types of errors as you can. in the context of class we are trying to acquaint you with as many concepts as possible, so for the sake of educational efficiency we will not be checking most errors in this lab, you may assume that your user provides correct input. you may add all appropriate error testing if you wish, but we will not be testing for it.

Im doing this last minute and literally none of my neighbors or people that my dad works with use excel so if anyone could me make up an example

Let r be a robotic arm with a fixed base and seven links. the last joint of r is a prismatic joint, the other ones are revolute joints. give a set of parameters that determines a placement of r. what is the dimension of the configuration space resulting from your choice of parameters?